Alright guys.
I have tested the Fiio A3 and SPL Crimson interface' (which is a very decent piece of gear) headphone outputs.
I have switched the headphones - KRK 6400 - back and forth many times and could not realistically notice difference in sound. What I heard was extremely similar sound. Technically, there IS some difference of course, because these are different pieces of gear. But I could not find it.
Also, when switching, I did not notice any hyped frequencies. To me, at default settings Fiio 3 has a flat EQ (you can flip a switch to add more bass).
For the very specific purpose I had in mind - tiny amp for headphones without a power supply - it works perfectly fine. I can now plug in AX8, turn it on, connect this little amp and play with headphones if I am away from a sound interface.
TL;DR - Fiio A3 works just fine with AX8.